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As an undergraduate student, I have worked on some projects for my own interest, and recently a professor said that one of these works can be published (in a Elsevier journal with impact factor of about 2). I personally think that this work is not strong enough to be published and included in my resume. (I don't have any prior experience in publishing and related stuff.)
Can a weak research article published in a journal affect my application for graduate school in a negative way?
There are very few circumstances under which I think it's a bad idea for undergraduates to write research papers. These primarily have to do with the quality of the journal: so long as it is a reputable, peer-reviewed journal, I wouldn't be too concerned with the "strength" of the work.
The reason is that publishing while an undergraduate—particularly as a primary author—demonstrates that you have already started to learn the basics of how to do research in your field. This means that you're less of an "unknown" quantity, and therefore less of a risk for a department reviewing your application. If you don't publish the research, then there's no tangible proof, and then you need to rely on your research supervisor to make that point in a letter of recommendation. (But then the question becomes: "if she could have written a paper, why didn't she?")
As for the exceptions above, so long as you don't publish in "vanity" journals (those which will publish basically anything, so long as people pay the appropriate publication "fees"), you should be fine.
I fully concur with the reply from aeismail but will add the following:
Publishing means your paper will go through peer-review. With a journal with impact=2 (reasonably respectable) you are likely to get a good set of revieweers. This will either lead to rejection or to suggestions for improvements. If publsihed the paper will likely be better than when it arrived at the journal. So remember that publishing includes more work than just sending something to be printed.
I think your supervisor may want to extend the research with more experiments, data, etc. This will lead to an much stronger paper.
Good journals often reject weak papers, or ask authors to make major changes to their manuscript. So it is hard to publish a weak paper in a good journal. But always remember that Many weak papers are improved to strong papers in the review process.
It is of course always much better to have publications in high impact journals, but this also depends on who is publishing. For a professor or post doc, the impact factor of the journal is very important.
However PhD student or undergraduate is usually understood as somebody who still cannot deserve a very high significance of they research work just by they competence and hard work. It is often looked just like a success and matters less. As a result, publications in low impact ( > 0 ! ) journals in this stage are also good enough.
